In this paper, based on a block splitting of the coe±cient matrix, we present a new generalized iterative method for solving the linear system Ax = b. This method is well-de¯ned even when some elements on the diagonal of A are zero. Convergence analysis and comparison theorems of the proposed method are provided. Specially, the results show that our new generalized AOR iterative method also, converges when A is an H-matrix. And for L-matrices, our new generalized Jacobi iterative method is faster than the classical Jacobi. The Numerical examples are also given to illustrate our results.

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